Difference between revisions of "2024 AMC 12A Problems/Problem 5"
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A data set containing <math>20</math> numbers, some of which are <math>6</math>, has mean <math>45</math>. When all the 6s are removed, the data set has mean <math>66</math>. How many 6s were in the original data set? | A data set containing <math>20</math> numbers, some of which are <math>6</math>, has mean <math>45</math>. When all the 6s are removed, the data set has mean <math>66</math>. How many 6s were in the original data set? | ||
Revision as of 17:30, 8 November 2024
Problem
A data set containing 
numbers, some of which are 
, has mean 
. When all the 6s are removed, the data set has mean 
. How many 6s were in the original data set?
Solution
Because the set has numbers and mean , the sum of the terms in the set is 
.
Let there be 
sixes in the set.
Then, the mean of this new set is 
. Equating this expression to and solving yields 
, so we choose answer choice 
.
See Also
| 2024 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
